Answer :
Final answer:
Using the tangent of the given angle of depression and the height of the lighthouse, we can calculate the distance from the base of the lighthouse to the ship. By solving the equation 186 ft / tan(18°), we find the distance to be approximately 582.47 feet.
Explanation:
This problem is an application of trigonometry, specifically the tangent function (tan). The tangent of an angle in a right triangle is defined as the opposite side over the adjacent side. Given the 186 ft lighthouse height (opposite side) and an angle of depression of 18°, we are asked to find the distance from the base of the lighthouse to the ship (adjacent side), using the tangent of 18°.
Here is how to solve it:
In the right triangle formed, the formula for tangent (opposite/adjacent) becomes tan(18°) = 186 ft/(distance to ship). You rearrange that equation to find the distance to the ship. After performing the calculation, it equates approximately to 186 ft / tan(18°), which is about 582.47 feet.
Therefore, the ship is approximately 582.47 feet away from the base of the lighthouse.
Learn more about Trigonometry here:
https://brainly.com/question/31896723
#SPJ11
